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In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm L p (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results. [ABSTRACT FROM AUTHOR]

Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the L p metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery. [ABSTRACT FROM AUTHOR]

In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C0(Ω0). As a corollary, we show that there is no ∈–isometry from any abstract M space with a strong unit into C0(Γ) if $$ 0 < \in < \frac{1} {9}. $$ [ABSTRACT FROM AUTHOR]

Letbe a unit sphere of thed-dimensional Euclidean space Rd and let(0 < p= 1) denote the real Hardy space onFor 0 < p= 1 andletEj(f,Hp) (j= 0, 1, ...) be the best approximation offby spherical polynomials of degree less than or equal toj, in the spaceGiven a distributionfonits Cesàro mean of order d>-1 is denoted byFor 0p. In this paper, the following result is proved:TheoremLet0N(f)˜BN(f)means that there’s a positive constant C, independent of N and f, such thatIn the cased= 2,this result was proved by Belinskii in 1996. [ABSTRACT FROM AUTHOR]

In this paper we use the T1 theorem to prove a new characterization with minimum regularity and cancellation conditions for inhomogeneous Besov and Triebel-Lizorkin spaces over spaces of homogeneous type. These results are new even for ℝ n. [ABSTRACT FROM AUTHOR]

In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator. [ABSTRACT FROM AUTHOR]

In this paper we characterize the boundedness and compactness of weighted composition operators of H∞ into α-Bloch spaces on the unit ball in ℂ n. [ABSTRACT FROM AUTHOR]

In this paper, the authors prove that if Ω satisfies a class of the integral Dini condition, then the parametrized area integral $$ \mu ^{\rho }_{{\Omega ,S}} $$ is a bounded operator from the Hardy space H 1(ℝ n ) to L 1(ℝ n ) and from the weak Hardy space H 1,∞(ℝ n ) to L 1,∞(ℝ n ), respectively. As corollaries of the above results, it is shown that $$ \mu ^{\rho }_{{\Omega ,S}} $$ is also an operator of weak type (1, 1) and of type ( p, p) for 1 < p < 2, respectively. These conclusions are substantial improvement and extension of some known results. [ABSTRACT FROM AUTHOR]

In this paper, we study the regularity of solutions for two–dimensional Cahn–Hilliard equation with non–constant mobility. Basing on the L p type estimates and Schauder type estimates, we prove the global existence of classical solutions. [ABSTRACT FROM AUTHOR]

In this paper, we determine the general solution of the functional equation f1(2 x + y) + f2(2 x − y) = f3( x + y) + f4( x − y) + f5( x) without assuming any regularity condition on the unknown functions f1, f2, f3, f4, f5 : ℝ → ℝ. The general solution of this equation is obtained by finding the general solution of the functional equations f(2 x + y) + f(2 x − y) = g( x + y) + g( x − y) + h( x) and f(2 x + y) + f(2 x − y) = g( x + y) + g( x − y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszú. The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi. [ABSTRACT FROM AUTHOR]

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows: in the critical case | c| = 1. By employing Mawhin's continuation theorem and some analysis techniques, some new results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the commutator generalized by a multiplier and a Lipschitz function. Under some assumptions, we establish the boundedness properties of it from L p(ℝ n) into $$ {\dot{F}^{{\beta ,\infty }}_{p} } $$ (ℝ n), the Triebel–Lizorkin spaces. [ABSTRACT FROM AUTHOR]

In this paper we present a mean value theorem derived from Flett’s mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value point. To answer what class of functions have this property, we consider a functional equation associated with this mean value theorem. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generation and propagation of interfaces for p-Laplacian equations with the derivative of a bi-stable potential. [ABSTRACT FROM AUTHOR]

The stability problems of the exponential (functional) equation on a restricted domain will be investigated, and the results will be applied to the study of an asymptotic property of that equation. More precisely, the following asymptotic property is proved: Let X be a real (or complex) normed space. A mapping f : X → ℂ is exponential if and only if f( x + y) – f( x) f( y) → 0 as ‖ x‖ + ‖ y‖ → ∞ under some suitable conditions. [ABSTRACT FROM AUTHOR]

In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C0(Ω0). As a corollary, we show that there is no ∈–isometry from any abstract M space with a strong unit into C0(Γ) if $$ 0 < \in < \frac{1} {9}. $$ [ABSTRACT FROM AUTHOR]

We study embeddings of spaces of Besov-Morrey type, [InlineMediaObject not available: see fulltext.], and obtain necessary and sufficient conditions for this. Moreover, we can also characterise the special weighted situation [InlineMediaObject not available: see fulltext.] for a Muckenhoupt $$\mathcal{A}_\infty$$ weight w, with w( x) = | x|, α > − d, as a typical example. [ABSTRACT FROM AUTHOR]

We investigate two classes of orthonormal bases for L2([0, 1) n). The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot piecewise linear spectral sequences and give an application of the first class of piecewise linear spectral sequences. [ABSTRACT FROM AUTHOR]

The author studies the L p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators. L p estimates, as well as the corresponding weighted estimates of such maximal functions, are obtained. Moreover, several applications of our results are highlighted. [ABSTRACT FROM AUTHOR]

The authors characterize the boundedness and compactness of composition operators between α-Bloch spaces of the unit ball. [ABSTRACT FROM AUTHOR]

We present the exact values of nonsquare constants, von Neumann–Jordan constants, Jung constants, packing constants, weakly convergent sequence coefficients and normal structure coefficients in a class of reflexive Orlicz function spaces and sequence spaces equipped with Luxemburg norm and Orlicz norm. [ABSTRACT FROM AUTHOR]

In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Øksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Itô type integrals and the fractional Black–Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed. [ABSTRACT FROM AUTHOR]

We consider the commutators of the Hörmander multiplier with CMO–functions on the Heisenberg group. The result of compactness on L p spaces is proved. [ABSTRACT FROM AUTHOR]

We prove that a u 0–concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u 0–concave operator under a weaker condition. [ABSTRACT FROM AUTHOR]

Let X be a (real or complex) Banach space with dimension greater than 2 and let ℬ0( X) be the subspace of ℬ( X) spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Φ on ℬ0( X) which preserve nilpotent operators in both directions. In particular, if X is infinite–dimensional, we prove that Φ has the form either Φ( T) = cATA−1 or Φ( T) = cAT'A−1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T' denotes the adjoint of T. As an application of these results, we show that every additive surjective map on ℬ( X) preserving spectral radius has a similar form to the above with | c| = 1. [ABSTRACT FROM AUTHOR]

A class of a posteriori parameter choice strategies for the operator version of Tikhonov regularization (including variants of Morozov's and Arcangeli's methods) is proposed and used in investigating the rate of convergence of the regularized solution for ill–posed nonlinear equation involving a monotone operator in Banach space. [ABSTRACT FROM AUTHOR]